-LRB- CNN -RRB- A Saudi-led coalition Tuesday ended its `` Operation Decisive Storm '' -- its nearly monthlong airstrike campaign in Yemen -- and a new initiative is underway .

`` Operation Renewal of Hope '' will focus on the political process .

Saudi Arabia had launched airstrikes on Houthi positions across Yemen , hoping to wipe out the Iranian-allied rebel group that has overthrown the government and seized power .

The Saudis say they want to restore the Yemeni government , a key U.S. ally in the fight against al Qaeda , which was kicked out of the capital by the rebels earlier this year .

This month , Saudi officials said airstrikes have degraded Houthi-controlled military infrastructure , including key buildings in the capital Sanaa .

The campaign achieved its objectives `` by a very good planning , very precise execution , by the courage of our pilots , our sailors , our soldiers , '' said Brig. Gen. Ahmed Asiri , a Saudi military spokesman .

A senior Saudi official told CNN that the Houthis agreed to `` nearly all demands '' of the U.N. Security Council . Former Yemeni President Ali Abdullah Saleh and his family will leave Yemen and never return for a position in politics , the source said .

A statement from the Saudi Embassy in Washington outlined objectives of the next phase of operations , including protecting civilians , enhancing humanitarian and medical assistance , confronting terrorism and creating an international coalition to provide maritime security .

Ground troops will continue to protect the border and confront any attempts to destabilize the situation , Asiri said . Military action will be taken if needed .

But beyond the military campaign , the Saudis and their allies have said they want to find a political solution for the violence-plagued nation .

The aim is to bring back Yemen 's `` security and stability through establishing a political process , '' said a statement from Saudi Arabia , the United Arab Emirates , Bahrain , Qatar and Kuwait .

Ousted Yemen President Abdu Rabu Mansour Hadi thanked the Saudi-led coalition . Hadi claims he 's Yemen 's legitimate leader and is working with the Saudis and other allies to return to his country .

`` We promise to restructure the Yemen military to ensure that it serves the people of Yemen , '' Hadi said , calling on the Houthis to withdraw , and saying that he would return to Yemen at `` the right time '' to rebuild the country .

`` You will witness many changes in the days to come in our mission to build an institutional government and military , far from rebel militancy , '' said Hadi .

Also Tuesday , a U.S. military official told CNN that the United States is conducting `` manned reconnaissance '' off Yemen . The official stressed that the repositioning of U.S. ships over the last days was not done to interdict Iranian ships , but to ensure freedom of navigation and maritime security .

Why is Saudi Arabia bombing Yemen ?

CNN 's Jethro Mullen , Tim Lister , Anas Hamdan , Jamie Crawford and journalist Hakim Almasmari contributed to this report .

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Former Yemeni President Ali Abdullah Saleh will leave , a source says

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Ousted leader Abdu Rabu Mansour Hadi promises to return

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Next phase , called `` Operation Renewal of Hope , '' will focus on political process